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18.A. Discuss the existence of both the deleted and the non-deleted limit e following functions at the point x = 0. . (a) f(x) = |¤], (b) f(x) == 1/x, *# 0, (c) f(x) = x sin (1/x), x * 0, (x sin (1/7). * + 0.

18.A. Discuss the existence of both the deleted and the non-deleted limit e following functions at the point x = 0. . (a) f(x) = |¤], (b) f(x) == 1/x, *# 0, (c) f(x) = x sin (1/x), x * 0, (x sin (1/7). * + 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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18.A

18.A. Discuss the existence of both the deleted and the non-deleted limits of the following functions at the point r = 0. (a) f(x) = |c|, * * 0, I sin (1/x), (x sin (1/x), [1, (b) f(x) = 1/x, (c) f(x) * + 0, x* 0, (d) f(x) 0, (e) f(x) sin (1/x), x * 0, 'ol x > 0. I<0, (f) f(x) = 18.B. Prove Lemma 18.2.
Transcribed Image Text:18.A. Discuss the existence of both the deleted and the non-deleted limits of the following functions at the point r = 0. (a) f(x) = |c|, * * 0, I sin (1/x), (x sin (1/x), [1, (b) f(x) = 1/x, (c) f(x) * + 0, x* 0, (d) f(x) 0, (e) f(x) sin (1/x), x * 0, 'ol x > 0. I<0, (f) f(x) = 18.B. Prove Lemma 18.2.
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